Lawmakers say the legislation will penalize federal agencies that fail to report records and incentivize states to send criminal history records to the National Instant Criminal Background Check System.

Cornyn, the No. 2 Republican, and Murphy, the most vocal Democrat on gun control, filed the measure after it was revealed that the Air Force didn't send Devin Kelley's court-martial and conviction for domestic violence to the FBI database used to approve gun buyers. They've dubbed the bill the "Fix NICS Act."

Kelley, who killed 26 people in a Texas church on Nov. 5, would not have been allowed to purchase a gun from a store if his records were in the database.

“For years, agencies and states haven’t complied with the law, failing to upload these critical records without consequence,” Cornyn said in a statement on Thursday. “Just one record that’s not properly reported can lead to tragedy, as the country saw last week in Sutherland Springs, Texas.”

In addition to Cornyn and Murphy, six other lawmakers from both parties are listed as cosponsors. They include Republican Sens. Tim Scott of South Carolina, Orrin Hatch of Utah and Dean Heller of Nevada; and Democratic Sens. Richard Blumenthal of Connecticut; Dianne Feinstein of California and Jeanne Shaheen of New Hampshire.

The measure is one of a handful introduced after two mass shootings in Las Vegas and Texas. With Congress generally gridlocked over gun control reforms, lawmakers say they've found common ground with the "Fix NICS Act."

And Cornyn tweeted that "law-abiding gun owners" should be allowed to purchase and possess firearms.

"But we must #FixNICS and enforce the laws already on the books prohibiting those convicted of violent acts from having guns," the tweet read.

L aw-abiding gun owners can and should be allowed to purchase and possess firearms. But we must #FixNICS and enforce the laws already on the books prohibiting those convicted of violent acts from having guns.

The measure has the support of the National Rifle Association -- a pro-Second Amendment group known to target lawmakers who buck its agenda.

"We applaud Sen. John Cornyn's efforts to ensure that the records of prohibited individuals are entered into NICS, while providing a relief valve for those who are wrongly included in the system," Chris Cox, executive director of the NRA, said in a statement Thursday.

Gun control and domestic violence advocates also applauded the legislation, marking the measure as a step toward congressional unity.

"Ensuring that the system contains updated records is necessary to keep guns out of the hands of dangerous individuals," Josh Horwitz, executive director of the Coalition to Stop Gun Violence, said in a statement. "We are encouraged by this bipartisan effort to improve NICS and save lives."

Just days after the church shooting, Sens. Jeff Flake, R-Ariz. and Martin Heinrich, D-N.M., filed legislation that would require the military to create a special category for domestic violence assault in its reporting to the national database.

Separately, the Senate Judiciary Committee has scheduled a hearing on the bump stock, the accessory that allows a rifle to fire at nearly automatic rates, and the background check system for Dec. 6.

It’s not clear if the NICS measure will be brought up in that hearing.